How can I connect a side with many vertices to a side with much fewer to produce a clean looking topology?
You are doing the correct thing - trying to reduce the amount of vertices on one side. That should work. The idea is to have as little of geometry as possible that would still hold the forms you need, because the fewer points and lines you have to worry about, the easier it is to work with them. You can see the opposite on the unexpected pinch where you have too much geometry so it's not that easy to smooth or correct. You have way too much unnecessary geometry there. I would delete a lot. 

In this particular situation it seems you might already have too much geometry to be able to replicate the forms. It is different from the reference object and you already have so many lines and vertices that it would be difficult to move them into places. 



These shapes needed to be addressed earlier in the modelling process. It might be easier to start over then to fix it. That might be frustrating, but I think everyone goes trough a lot of redoing when learning this. I certainly did. With this kind of object it may be hard to understand what the forms are, so I would start by establishing all the lines that I understand from the start(in 3d). I would only make a vertex and extrude it into lines and check the position looking from multiple sides, like from top and side views. Then I would try to connect them and this way I could add or remove points as needed while connecting the lines.  I would aim to use only as many vertices as it is needed and not one more carefully observing if the forms generated by Subsurf modifier are matching the reference. I cannot advise any further without actually modelling the thing I am afraid.